Solving the Equation 2(w + 3w) = 64: A Step-by-Step Guide with Common Problems Explained

Understanding and Solving the Equation 2(w + 3w) = 64

Understanding the Context

Equations are fundamental tools in algebra that help us find unknown values by balancing expressions. One common type is linear equations involving parentheses and combined like terms. An equation like 2(w + 3w) = 64 might seem simple, but mastering its solution builds a strong foundation for more complex math concepts.

If you're learning algebra or reviewing linear equations, solving something like 2(w + 3w) = 64 helps develop essential problem-solving skills. In this article, we’ll break down the steps to solve this equation, explain why each step matters, and clarify any common pitfalls students encounter.

Step 1: Simplify the Expression Inside the Parentheses

Key Insights

Start by combining like terms inside the parentheses:
w + 3w = 4w

So the equation becomes:
2(4w) = 64

This simplification is crucial—it reduces complexity and reveals the equation’s true form: 8w = 64

Step 2: Isolate the Variable w

🔗 Related Articles You Might Like:

📰 Uncover/Obscure: The Hidden Secrets No One Is Talking About (Obscure Far 🔍) 📰 Obscure Beyond Belief: What’s Obscure Will Shock You Silently! 📰 Discover the Obscure World Everyone Overlooks—These Sites Will Blow Your Mind! 📰 The Bare Picture That Shocked The Fanbase Selena Gomez Stripped Down In Infamous Exposing Moment 📰 The Barefoot Look Sabrina Carpenter Is Using To Turn Every Boys Knees Into Jello 📰 The Bargain Rewired This Ross Deal Shocks Everyone With 49 Cent Magic 📰 The Beautiful Birth Flower Of September Revealedmore Than Just A Bloom 📰 The Beautiful Moment When Day Ends Infinal Glow 📰 The Beautiful Truth About Puglia Italy Youre Not Supposed To Know 📰 The Belt Thats Slipping Without You Noticedanger Lurks Beneath The Surface 📰 The Bestseller Quince Review Reveals Secrets No Ones Talking About 📰 The Bet I Made With Sabrina Carpenter Her Booty Changed My Entire Nightyoull Witness It Yourself 📰 The Betrayal Deepened By A Forbidden Bond 📰 The Big Reason Roowe Furniture Is Taken Over By Interior Kings And Queens 📰 The Billion Dollar Secret Behind Ryan Trahans Net Fortune Exploded 📰 The Binomial Probability Formula Is 📰 The Bitter Showdown Royals Vs The Brewersand The Truth Bites Hard 📰 The Bizarre Day Rachel Jade Stripped Down And The World Went Wild

Final Thoughts

To solve for w, divide both sides of the equation by 2:
(8w)/2 = 64/2
4w = 64

Dividing by the coefficient of w isolates the variable, making it easier to find its value. (Always divide both sides by the same number to maintain equation balance.)

Step 3: Solve for w by Dividing Both Sides by 4

Now divide both sides by 4:
4w ÷ 4 = 64 ÷ 4
w = 16

This final step gives you the value of w. Always check your solution by substituting w = 16 back into the original equation.

Step 4: Verification — Plug the Solution Back In

Substitute w = 16 into 2(w + 3w) = 64:
Left side:
2(16 + 3×16) = 2(16 + 48) = 2(64) = 128
Wait — that’s not equal to 64!

But hold on—let’s double-check the arithmetic carefully: